I’m not too current on the state of Flash these days, but last time I worked with it, there were considerable accessibility issues. Once you get beyond the “Flash can do animation better,” you end up with a few things:

HTML5 and CSS3 are open. This means that the community oversees the development and future of the languages. Flash is not.

HTML5 provides you with with semantic hooks to actually describe your content – even for blind users. Does Flash?

Apple put an enormous stake into Adobe’s heart when they announced that the iPhone wouldn’t support Flash. This is huge. The number of mobile browsers is increasing exponentially every single year. It would be crazy to ignore those users, or provide them with a text fallback version of your site.

In general, I don’t think developers really like to work with Flash. Honestly, I hated it.